Japanese Journal of Applied Physics Vol. 43, No. 1, 2004, pp. 247–248 #2004 The Japan Society of Applied Physics

Short Note

A Discussion of the Practical Importance of Positron Annihilation Lifetime Spectroscopy Percolation Threshold in Evaluation of Porous Low-K Dielectrics Konstantin P. M OGILNIKOV, Mikhail R. BAKLANOV
, Denis SHAMIRYAN1 and Mihail P. P ETKOV2 Interuniversity Microelectronic Center (IMEC), Leuven, Belgium 1 IMEC and Electrical Engineering Department of Catholic University of Leuven, Belgium 2 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA (Received July 22, 2003; revised September 20, 2003; accepted September 29, 2003; published January 13, 2004)

The pore connectivity threshold (percolation threshold) in porous low-K dielectric films measured by Positron Annihilation Lifetime Spectroscopy (PALS) reflects only the interconnectivity of mesopores (2–50 nm size). Here we show direct evidence for molecular (toluene) diffusion at porosity values significantly below the PALS’s percolation threshold. Therefore, the pores are still interconnected through intrinsic micropores (<2 nm) in the low-K film matrix. This implies that fundamental limitations may exist in the evaluation of pore interconnectivity and the integrity of diffusion barriers deposited on top of porous low-K films by the detection of Ps escape. [DOI: 10.1143/JJAP.43.247] KEYWORDS: low-K dielectric films, pore connectivity, diffusion, PALS

One of the most important limitations for the use of porous low-K films as interlevel dielectrics in advanced ULSI technology is the difficulty in manufacturing materials with closed pores. For this reason, results of recent investigations of pore interconnectivity by positron annihilation lifetime spectroscopy (PALS) have attracted a lot of interest and have stimulated discussions. It was reported that PALS can be used to distinguish the fraction of open and closed pores and to determine the interconnectivity threshold.1–3) We show that the closed pores measured by PALS have a relative meaning and they are not necessarily closed for diffusion of Cu and other molecules used during the technological steps. In PALS, positrons implanted in insulators form positronium (Ps) in singlet (para-Ps) and triplet (ortho-Ps) states. The lifetime of ortho-positronium (o-Ps) localized in the pores correlates with the pore size.2) The macropore PALS data (>50 nm) have been calibrated by adsorption porosimetry, whereas the quantum mechanical model developed by Tao and Eldrup (TE) is used for size derivation of micropores. Recently, significant progress has been made in the measurement of mesopores, which are a characteristic of most low-K films. However, in films with multimodal porosity, differences in Ps ground state energies4) must be taken into account for a proper description of phenomena related to o-Ps movement between pores with different sizes. For a more detailed discussion of the Ps kinetics and interaction with porous dielectrics, see refs. 4 and 5. 1 mm thick Methylsilsesquioxane (MSSQ) based porous low-K films with different porosity values were deposited on top of silicon wafers. Ellipsometric porosimetry6) showed that these films have bimodal porosity with constitutive micropores and artificial mesopores. The porogen concentration well correlates with the volume of artificial mesopores.7) According to PALS, these films show a percolation threshold at the porogen concentration close to 25%.8) It is believed that films with porosity below the percolation threshold have non interconnected pores. To examine the physical meaning of the PALS percolation threshold, diffusion of condensed toluene in these films was studied in the following manner. Dense CVD Si3 N4

films were deposited on top of the porous films. Then, the samples were dipped in liquid toluene. The toluene penetration from the sample edge gradually changed the color of the film due to the change in film refractive index (Fig. 1). The penetration depth as a function of the dipping time was measured using an optical microscope. PALS measurements of varieties of MSSQ-based low-K films have reportedly shown a connectivity threshold between 15% and 25% porosity.1,8–10) For the films evaluated in this study, the reported percolation threshold was close to 25% porosity.8) The toluene diffusion length depends on the dipping time and porosity (Fig. 2). A sharp increase in diffusion length was observed starting from the porogen concentration close to 20%. However, the toluene diffusion was still significant when the films were prepared with smaller porogen concentration. For instance, the diffusion length during 5 min. was 67 mm for the lowest porogen concentration (1%) (Figs. 1 and 2). This value is significantly larger than the film thickness and therefore only 4–5 s. are required for complete ‘‘wetting’’ of the film. The sharp increase in diffusivity at the porogen concentration close to 20%, which correlates with the PALS percolation threshold, is related to the interconnection of the mesopores as was shown in ref. 7 when the

67 µm Fig. 1. Toluene diffusion length in MSSQ-based low-K film prepared with porogen concentration of 1%.




Corresponding author. E-mail address: [email protected] 247

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1400

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Fig. 2. Toluene diffusion length versus exposure time for MSSQ-based low-K films with different porogen concentration.

same films were evaluated by ellipsometric porosimetry. The coexistence of micro- and mesopores requires careful consideration of the pore connectivity on a sub-nanometer scale. The transition from a micropore to a mesopore is associated with a gain of kinetic energy, equal to the difference in Ps binding energy.4,5) The gained energy is lost rapidly (within a small fraction of the o-Ps lifetime) through collisions with the walls. After several collisions, even an epithermal Ps remains localized to the larger volume. The reverse transition from a mesopore to a micropore is strongly suppressed because it requires significant energy (eV) to overcome the difference in Ps binding energy. PALS experiments detect the final state of the system after diffusion and trapping in mesopores have occurred. A detailed discussion of the Ps trapping kinetics is given in ref. 5. Here, we use a simple quantum-mechanical model to show the origin of this irreversible directional transition. The Ps ground level can be estimated as Eo ¼
2 h2 =2ml2 ;

ð1Þ

where h is Plank’s constant, m is the Ps mass and l is the size of the potential well. According to eq. (1), the o-Ps ground level in a potential well with a diameter of 10 nm is two orders of magnitude lower than that in a well with a diameter of 1 nm (Eo ¼ 1:87  103 eV and 1:87  101 eV, respectively) (Fig. 3). The mean o-Ps energy in large pores at room 20 Energy of ground state

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Fig. 3. o-Ps ground state energy in pores with different sizes.

temperature is close to kT (2:5  102 eV). Movement of oPs between pores with different sizes requires a change in energy and the probability of the movement is proportional to expððE02  E01 Þ=kTÞ. Therefore, o-Ps has the possibility of easy movement in pores larger than 3–5 nm and from small pores to large pores. If o-Ps is able to escape to vacuum and show a natural lifetime of 142 ns, one can conclude that the large pores are interconnected. The situation is opposite for diffusion from large pores to micropores. The diffusion of o-Ps localized in the large pores (>3 nm) to subnanometer pores requires significant activation energy (of the order of a few eV) that depends on the size of the micropores (Fig. 3). This renders the probability for such transition negligible. As mentioned above, the foamed MSSQ based films contain both micro- and mesopores. Although both types generate distinct PALS signals, according to the above analysis, o-Ps localized in mesopores virtually cannot escape from the film through the micropores, whereas other species may be able to do so. Comparison of these data with results obtained by PALS allows us to conclude that the PALS’s percolation threshold is only related to the interconnection of mesopores. Therefore, the practical importance of the PALS’s percolation threshold is limited from the point of view of penetration, diffusion, and adsorption of Cu and molecules used for deposition, etching, and cleaning. The quantummechanical nature of the o-Ps transition from meso- to micropores also suggests that PALS evaluation of the integrity of diffusion barriers deposited on top of porous low-K films may be limited to openings on the mesopore scale (2 nm). These can still facilitate gas, solvent, and Cu diffusion. The conclusions have been supported by the results of experiments with diffusion of different molecules in various porous films. More detailed analysis of these results will be published elsewhere. It is our pleasure to thank Dr. Thomas Abell of INTEL for fruitful discussions and useful comments. 1) C. L. Wang, M. H. Weber, K. G. Lynn and K. P. Rodbell: Appl. Phys. Lett. 81 (2002) 4413. 2) T. L. Dull, W. E. Frieze, D. W. Gidley, J. N. Sun and A. F. Yee: J. Phys. Chem. B 105 (2001) 4657. 3) M. P. Petkov, M. Weber, K. G. Lynn and K. P. Rodbell: Appl. Phys. Lett. 79 (2001) 3884. 4) T. Goworek: J. Nucl. Radiochem. Sci. 1 (2000) 11. 5) M. P. Petkov, C. L. Wang, M. Weber, K. G. Lynn and K. P. Rodbell: J. Phys. Chem. B 107 (2003) 2725. 6) M. R. Baklanov, K. P. Mogilnikov, V. P. Polovinkin and F. N. Dultsev: J. Vac. Sci. Technol. B 18 (2000) 1385. 7) M. R. Baklanov, C. Jehoul, C. M. Flannery, K. P. Mogilnikov, R. Gore, D. Gronbeck, G. Prokopowicz, C. Sullivan, Y. You, N. Pugliano and M. Gallagher. Proc. Advanced Metallization Conference, MRS, 2002, p. 273. 8) Shipley Public Presentation, 2001; Shipley Press Release. 9) Y. F. Hu, D. W. Gidley, J. N. Sun and W. E. Frieze. SEMATECH’s Ultra Low-K Workshop, SF, 2002. 10) A. M. Padovani, L. Rhodes, S. A. B. Allen and P. A. Kohl. J. Electrochem. Soc. 149 (2002) F171.